A Bayesian approach to sequential monitoring of nonlinear profiles using wavelets

Roumen Varbanov, Eric Chicken, Antonio Linero, Yun Yang

Research output: Contribution to journalArticle

Abstract

We consider change-point detection and estimation in sequences of functional observations. This setting often arises when the quality of a process is characterized by such observations, called profiles, and monitoring profiles for changes in structure can be used to ensure the stability of the process over time. While interest in phase II profile monitoring has grown, few methods approach the problem from a Bayesian perspective. We propose a wavelet-based Bayesian methodology that bases inference on the posterior distribution of the change point without placing restrictive assumptions on the form of profiles. By obtaining an analytic form of this posterior distribution, we allow the proposed method to run online without using Markov chain Monte Carlo (MCMC) approximation. Wavelets, an effective tool for estimating nonlinear signals from noise-contaminated observations, enable us to flexibly distinguish between sustained changes in profiles and the inherent variability of the process. We analyze observed profiles in the wavelet domain and consider two possible prior distributions for coefficients corresponding to the unknown change in the sequence. These priors, previously applied in the nonparametric regression setting, yield tuning-free choices of hyperparameters. We present additional considerations for controlling computational complexity over time and their effects on performance. The proposed method significantly outperforms a relevant frequentist competitor on simulated data.

Original languageEnglish (US)
Pages (from-to)761-775
Number of pages15
JournalQuality and Reliability Engineering International
Volume35
Issue number3
DOIs
StatePublished - Apr 1 2019

Fingerprint

Monitoring
Markov processes
Computational complexity
Tuning
Wavelets
Bayesian approach
Change point
Posterior distribution

Keywords

  • Bayesian
  • phase II
  • profile monitoring
  • statistical process control
  • wavelets

ASJC Scopus subject areas

  • Safety, Risk, Reliability and Quality
  • Management Science and Operations Research

Cite this

A Bayesian approach to sequential monitoring of nonlinear profiles using wavelets. / Varbanov, Roumen; Chicken, Eric; Linero, Antonio; Yang, Yun.

In: Quality and Reliability Engineering International, Vol. 35, No. 3, 01.04.2019, p. 761-775.

Research output: Contribution to journalArticle

Varbanov, Roumen ; Chicken, Eric ; Linero, Antonio ; Yang, Yun. / A Bayesian approach to sequential monitoring of nonlinear profiles using wavelets. In: Quality and Reliability Engineering International. 2019 ; Vol. 35, No. 3. pp. 761-775.
@article{a9f931e7097f42be8bd0402a6664e820,
title = "A Bayesian approach to sequential monitoring of nonlinear profiles using wavelets",
abstract = "We consider change-point detection and estimation in sequences of functional observations. This setting often arises when the quality of a process is characterized by such observations, called profiles, and monitoring profiles for changes in structure can be used to ensure the stability of the process over time. While interest in phase II profile monitoring has grown, few methods approach the problem from a Bayesian perspective. We propose a wavelet-based Bayesian methodology that bases inference on the posterior distribution of the change point without placing restrictive assumptions on the form of profiles. By obtaining an analytic form of this posterior distribution, we allow the proposed method to run online without using Markov chain Monte Carlo (MCMC) approximation. Wavelets, an effective tool for estimating nonlinear signals from noise-contaminated observations, enable us to flexibly distinguish between sustained changes in profiles and the inherent variability of the process. We analyze observed profiles in the wavelet domain and consider two possible prior distributions for coefficients corresponding to the unknown change in the sequence. These priors, previously applied in the nonparametric regression setting, yield tuning-free choices of hyperparameters. We present additional considerations for controlling computational complexity over time and their effects on performance. The proposed method significantly outperforms a relevant frequentist competitor on simulated data.",
keywords = "Bayesian, phase II, profile monitoring, statistical process control, wavelets",
author = "Roumen Varbanov and Eric Chicken and Antonio Linero and Yun Yang",
year = "2019",
month = "4",
day = "1",
doi = "10.1002/qre.2409",
language = "English (US)",
volume = "35",
pages = "761--775",
journal = "Quality and Reliability Engineering International",
issn = "0748-8017",
publisher = "John Wiley and Sons Ltd",
number = "3",

}

TY - JOUR

T1 - A Bayesian approach to sequential monitoring of nonlinear profiles using wavelets

AU - Varbanov, Roumen

AU - Chicken, Eric

AU - Linero, Antonio

AU - Yang, Yun

PY - 2019/4/1

Y1 - 2019/4/1

N2 - We consider change-point detection and estimation in sequences of functional observations. This setting often arises when the quality of a process is characterized by such observations, called profiles, and monitoring profiles for changes in structure can be used to ensure the stability of the process over time. While interest in phase II profile monitoring has grown, few methods approach the problem from a Bayesian perspective. We propose a wavelet-based Bayesian methodology that bases inference on the posterior distribution of the change point without placing restrictive assumptions on the form of profiles. By obtaining an analytic form of this posterior distribution, we allow the proposed method to run online without using Markov chain Monte Carlo (MCMC) approximation. Wavelets, an effective tool for estimating nonlinear signals from noise-contaminated observations, enable us to flexibly distinguish between sustained changes in profiles and the inherent variability of the process. We analyze observed profiles in the wavelet domain and consider two possible prior distributions for coefficients corresponding to the unknown change in the sequence. These priors, previously applied in the nonparametric regression setting, yield tuning-free choices of hyperparameters. We present additional considerations for controlling computational complexity over time and their effects on performance. The proposed method significantly outperforms a relevant frequentist competitor on simulated data.

AB - We consider change-point detection and estimation in sequences of functional observations. This setting often arises when the quality of a process is characterized by such observations, called profiles, and monitoring profiles for changes in structure can be used to ensure the stability of the process over time. While interest in phase II profile monitoring has grown, few methods approach the problem from a Bayesian perspective. We propose a wavelet-based Bayesian methodology that bases inference on the posterior distribution of the change point without placing restrictive assumptions on the form of profiles. By obtaining an analytic form of this posterior distribution, we allow the proposed method to run online without using Markov chain Monte Carlo (MCMC) approximation. Wavelets, an effective tool for estimating nonlinear signals from noise-contaminated observations, enable us to flexibly distinguish between sustained changes in profiles and the inherent variability of the process. We analyze observed profiles in the wavelet domain and consider two possible prior distributions for coefficients corresponding to the unknown change in the sequence. These priors, previously applied in the nonparametric regression setting, yield tuning-free choices of hyperparameters. We present additional considerations for controlling computational complexity over time and their effects on performance. The proposed method significantly outperforms a relevant frequentist competitor on simulated data.

KW - Bayesian

KW - phase II

KW - profile monitoring

KW - statistical process control

KW - wavelets

UR - http://www.scopus.com/inward/record.url?scp=85055116954&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85055116954&partnerID=8YFLogxK

U2 - 10.1002/qre.2409

DO - 10.1002/qre.2409

M3 - Article

VL - 35

SP - 761

EP - 775

JO - Quality and Reliability Engineering International

JF - Quality and Reliability Engineering International

SN - 0748-8017

IS - 3

ER -